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TWO QUEUES IN TANDEM WITH RETRIAL CUSTOMERS

Published online by Cambridge University Press:  27 July 2001

Evangelos Moutzoukis  and
Christos Langaris
Evangelos Moutzoukis
Affiliation:
Department of Mathematics, University of Ioannina, Ioannina 45 110, Greece, E-mail: clagar@cc.uoi.gr
Christos Langaris
Affiliation:
Department of Mathematics, University of Ioannina, Ioannina 45 110, Greece, E-mail: clagar@cc.uoi.gr
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Abstract

We consider two single-server queues in tandem. The customers receive service at the first station and then they proceed to the second. There are no intermediate waiting positions and, so, the blocking phenomenon is observed. The arriving customers who find the first station unavailable (busy or blocked) behave like retrial customers. We consider the case of “constant retrial policy.” For such a system, we obtain the system state probabilities in steady state in terms of generating functions. We present also some interesting measures of the system performance and directly deduce results for the corresponding ordinary (without retrials) model. We consider, finally, the special case of exponential service times as an example.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 15 , Issue 3 , July 2001 , pp. 311 - 325
Copyright
© 2001 Cambridge University Press

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